Supersimmetria, naturalezza e selezione ambientale

1. Supersimmetria, naturalezza e selezione ambientale G.F. Giudice N. Arkani-Hamed, G.F.G., R. Rattazzi, in preparation N. Arkani-Hamed, A. Delgado, G.F.G., NPB 741, 108 (2006) Delgado, G.F.G., PLB 627, 155 (2005) N. Arkani-Hamed, S. Dimopoulos, G.F.G., A. Romanino, NPB 709, 3 (2005) N. Arkani-Hamed, S. Dimopoulos, JHEP 0506, 073 (2005) G.F.G., A. Romanino, NPB 699, 65 (2004)

2. Central problem of particle physics: H2 very sensitive to high-energy corrections No large tuning   < TeV Can mH ~ 180220 GeV reduce the tuning? NO! Abuse of effective theories: finite (or log-div) corrections at remain Ex.: in SUSY quadratic divergences cancel, but

3. Naturalness  < 1 TeV search for new physics n Cancellation of Existence of electron self-energy +-0 mass difference KL-KSmass difference gauge anomaly cosmological constant positron  charm top 10-3 eV?? CAVEAT EMPTOR

4. Supersymmetry: triumph of symmetry concept! • Gauge-coupling unification • Dark Matter • Radiative EW breaking

5. broken phase unbroken phase H2 SM Hierarchy: a problem of criticality Exact supersymmetry  on critical point Small breaking of supersymmetry 

6. In supersymmetry: less than 10% tuning ~ Higgs mass ~ The theory is tuned at few % or worse (not much wrt (MW/MGUT)2~10-28, but it bites into LHC territory)

7. EW breaking computable as a function of soft terms In natural supersymmetry: MS<<Qc<<MPl and MZ~MS Little hierarchy only if Qc~MS

8. A measure of the fine tuning • A characterization of the tuning

10. DARK MATTER Natural thermal relic with DMh2=0.1270.010 Quantitative difference after LEP & WMAP For MS>MZ : neutralino is almost pure state B-ino: annihilation through sleptons (too slow): me < 110 GeV (LEP: me > 100 GeV) H-ino, W-ino: annihilation through gauge bosons (too fast) ~ ~

11. DM is possible in “special” regions: • coannihilation • Higgs resonance • “Well-tempered” • or non-thermal Both MZ and DM can be reproduced by low-energy supersymmetry, but at the price of some tuning. Unlucky circumstances or wrong track?

12. Could God have made the Universe in a different way? Does the necessity of logical simplicity leave any freedom at all? What determines the physical laws? The reductionist’s dream: Unique consistent theory defined by symmetry properties (no deformation allowed, no free parameters) • Monotheistic view God • M-theoristic view  2nd string revolution String theory  low-energy susy  SM

13. A different point of view Vacuum structure of string theory ~ 10500 vacua (N d.o.f in M config. make MN) Expansion faster than bubble propagation Big bang universe expanding like an inflating balloon Unfolding picture of a fractal universe multiverse

14. Not a unique “final” theory with parameters = O(1)  allowed by symmetry but a statistical distribution In which vacuum do we live? Determined by “environmental selection” • Large and positive  blows structures apart • Large and negative  crunches the Universe too soon  Weinberg Is the weak scale determined by “selection”? Are fermion masses determined by “selection”? Will these ideas impact our approach to the final theory? I will show two examples relevant to supersymmetry and LHC

15. “A physicist talking about the anthropic principle runs the same risk as a cleric talking about pornography: no matter how much you say you are against it, some people will think you are a little too interested” S. Weinberg In 1595 Kepler asked the question “Why are there 6 planets?”It seems a proper scientific question ( “Why are there 3 quark families?” )

16. “Mysterium Cosmographicum” gives a geometrical explanation Sphere Cube Tetrahedron Dodecahedron Icosahedron Octahedron Sphere Saturn Jupiter Mars Earth Venus Mercury Planetary orbits lie within the only 5 Platonic solids that can be both circumscribed and inscribed within a sphere. It well matched planetary distances known at that time. We are confident about the anthropic explanation because we observe a vast universe with a multitude of stars The ultimate Copernican revolution?

17. Susy prefers to be broken at high scale • Prior sets an upper bound on MS Susy near-critical Assume mi=ci MS, and MS scans Qc = MPl f(ci,a) does not depend on MS MS>Qc <H> = 0, MS<Qc <H>  0 Impose prior that EW is broken (analogy with Weinberg) Loop factor < ln MS/Qc> Little hierarchy: Supersymmetry visible at LHC, but not at LEP (post-diction)

19. If  and MS scan independently: • solution to  problem • prediction for  and tan

20. SM + gauginos + higgsinos at TeV Squarks + sleptons at m ~ With respect to ordinary susy: • no FCNC, no excessive CP • dim-5 proton decay suppressed • heavier Higgs boson A more radical approach: Split Supersymmetry ABANDON NATURALNESS BUT REQUIRE: • Gauge-coupling unification • Dark matter

21. Gauge-coupling unification as successful (or better) than in ordinary SUSY

22. Not unique solution, however… • Minimality: search for unification with single threshold, only fermions in real reps, and 1015 GeV < MGUT < 1019 GeV  SpS has the minimal field content consistent with gauge-coupling unification and DM • Splitting of GUT irreps: in SpS no need for new split reps either than SM gauge and Higgs • Light particles: R-symmetry protects fermion masses • Existence and stability of DM: R-parity makes c stable • Instability of coloured particles: coloured particles are necessary, but they decay either by mixing with quarks (FCNC!) or by interactions with scale < 1013 GeV • SpS not unique, but it has all the necessary features built in

23. R-symmetry “splits” the spectrum (Mgand m mix through renorm.) • R-invariant  dim = 2 R-violating  dim = 3 ~ Why Supersymmetry?

24. Analogy: in SM, L not imposed but accidental. mn small, although L-breaking is O(1) in underlying theory • In supergravity, m not generated at O(MPl) but only O(MS2/MPl) • Here, Mg and m not generated at O(m) but only O(m2/M*) ~ ~ ~ Split Supersymmetry determined by susy-breaking pattern

25. ~ m3/2 and m are in general independent parameters of SpS Unavoidable R-breaking from CC cancellation Potentially larger effect from anomaly med. Eq. motion for conformal compensator In theories where susy breaking is tied to gravity and supersymmetry is restored in the flat limit, Ff 0

26. Higgs mass • Gluino lifetime • Gaugino couplings • Electric dipole moments • Dark Matter How to test Split Supersymmetry: HIGGS MASS

27. arg ( u d M ) * * ~ ~ g g ELECTRIC DIPOLE MOMENTS Exp: de<2 10-27 ecm dn<6 10-26 ecm Yale: de ~10-29 10-31 Sussex: de ~10-30 Los Alamos: de dn ~10-31 10-35 BNL: d ~ 10-24

28. In SUSY, gauge (g) and gaugino ( ) couplings are equal ~ ~ ~ ~ ~ g g g g g • Fit of M, , u , d from  cross section and distributions • H final states • BR( H) At LHC ( / g -1) = 0.2 - 0.5 At ILC ( / g -1) = 0.01 - 0.05 GAUGINO COUPLINGS

29. GLUINO LIFETIME Age of the universe Gamma rays Nucleosynthesis Decays outside detector Gluino hadronizes • Charged R-hadrons. Time delay & anomalous ionization energy loss. At LHC, M<2.5 TeV. Mass resolution better than 1% • Neutral R-hadrons. Tagged jet M<1.1 TeV. Once tagged, identify gluino small energy deposition • Flippers. Difficulty in tagging • Gluinonium. M<1 TeV, direct mass reconstruction • Stopped gluinos. Possibility of measuring long lifetimes

30. DARK MATTER • Higgsino =1.0--1.2 TeV • W-ino M2=2.0--2.5 TeV • B-ino/Higgsino M1~ • B-ino/W-ino M1~M2 • Higgs resonance M=mH • Gravitino induced Present limit: 10-41 --10-42 cm2 Future sensib.: 10-44 --10-45 cm2

31. CONCLUSIONS • Supersymmetry is still the best candidate to overthrow the SM, but it suffers from tunings at the level of % • Absence of new discoveries at LEP, failure to explain the cosmological constant, and developments in string landscape suggest a possible change of approach to the final theory • Can we test “anthropic” solutions?